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On the Stability of Systems of Linear Differential Equations of Neutral Type with Distributed Delay

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Abstract

We consider one class of systems of nonautonomous linear differential equations of neutral type with distributed delay. We obtain sufficient conditions for the exponential stability of the zero solution and conditions on perturbations of the coefficients under which the exponential stability of the zero solution is preserved. Using a Lyapunov—Kjasovskiĭ functional of a special kind, we prove some estimates that characterize the exponential decay of solutions at infinity.

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Acknowledgments

The author is deeply grateful to G. V. Demidenko, I. I. Matveeva, and M. A. Skvortsova for their attention and valuable advices. The author also expresses his gratitude to the referee for remarks and recommendations.

Funding

The author was supported by the Russian Foundation for Basic Research (project no. 18-29-10086).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    T. Yskak

  2. Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090, Russia

    T. Yskak

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  1. T. Yskak
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Correspondence to T. Yskak.

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Russian Text © The Author(s), 2019, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2019, Vol. XXII, No. 3, pp. 118–127.

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Yskak, T. On the Stability of Systems of Linear Differential Equations of Neutral Type with Distributed Delay. J. Appl. Ind. Math. 13, 575–583 (2019). https://doi.org/10.1134/S1990478919030177

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  • DOI: https://doi.org/10.1134/S1990478919030177

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